Slice the sweet onions thin so they cook evenly.
Add the sliced onions to a dry nonstick pan over medium heat, cover, and let steam for 6-8 minutes, until softened and translucent.
Uncover and add the butter and a drizzle of olive oil once most of the water has cooked off and light browning starts on the bottom of the pan. Stir constantly from here, keeping the onions moving so they caramelize evenly.
Continue cooking, stirring often, until deeply browned and jammy — about 30 minutes for classic caramelized onions, closer to 40 for a deeply reduced, jammy texture.
Season well with salt toward the end.